Long range missile programmer

ABSTRACT

1. In an apparatus for controlling the flight trajectory of a guided missile, second order programming computer and smoother means for manipulating input perameters in accordance with the relations   AND EI Et + k(t) (Dr-Dm) Et + F(d) WHERE EO IS THE OUTPUT DATA FROM SAID COMPUTER, EI IS THE INPUT DATA TO SAID COMPUTER, EO IS THE FIRST DERIVATIVE OF EO omega N IS THE GAIN SENSITIVITY FACTOR OF THE COMPUTER, ET is the elevation of the target, sigma IS A CONSTANT, P is the present time, C is the time of guidance initiation, K(T) IS A TIME VARYING PROGRAMMING FACTOR AND F(d) is the output of an input driving function generator, a first input source of voltage for said second order programming computer means relating to ET, driving function generator means F(d) electrically coupled to and directed as a second input to said second order programming computer means, said driving function generator means comprising a climb-cruise phase generator in series with a terminal phase generator, means within said climb-cruise phase generator to produce an output function

nited States Patent [191 Schroader et al.

[ 1 LONG RANGE MISSILE PROGRAMMER [75] inventors: Irvin H. Schroader,Simpsonville;

Melvin E. Hosea, Silver Spring; Vincent J. Caggiano, Rockville; Leo C.Miller, Silver Spring, all of Md.

[73] Assignee: The United States. of America as represented by theSecretary of the Navy, Washington, D.C.

[22] Filed: May 15, 1961 [21] Appl. No.2 110,615

Primary ExaminerSamue1 Feinberg Attorney-W. O. Quesenberry, ClaudeFunkhouser and Gilber G. Kovelman EXEMPLARY CLAIM in an apparatus forcontrolling the flight trajectory of a guided missile, second orderprogramming computer and smoother means for manipulating inputperameters in accordance with the relations constant where e, is theoutputdata from said compute r,= e, is the input data to said computer,

e is the first derivative of-e am is the gain sensitivity factor of thecomputer, E is the elevation of the target, a is a constant, P is thepresenttime, C is the time of guidance initiation, k(t) is a timevarying programming factor and F(d) is the output of an input drivingfunction [111 3,741,52 June 26, 1973 generator, a first input source ofvoltage for said second order programming computer means relating to Edriving function generator means F(d) electrically coupled to anddirected as a second input to said second order programming computermeans, said driving function generator means comprising a climb-cruisephase generator in series with a terminal phase generator, means withinsaid climb-cruise phase generator to produce an output functionF(t)=(bE(;aaDm)/b+Dm) where F(t) is the program variable defining theclimb and cruise phases,

D is the slant range to the missile,

E is the initial condition elevation angle of the guidance transmitter,and

a and b are constants, the output of said climb-cruise phase generatorbeing directed as a first input to said terminal phase generator, meanselectrically connected to the input of said terminal phase generatorproviding a second input to said terminal phase generator relating to Efeedback means electrically connected to the output of said terminalphase generator to feed back the output F (d) of said driving functiongenerator as a third input to said terminal phase generator, means.within said terminal phase generator for acting upon said first, secondand third inputs prior to terminal phase initiation to produce an outputfunction k(t) I: [F(d) ET mun/l,

means within said terminal phase generator to render ineffective saidfirst, second and third inputs upon terminal phase initiation, meanswithin said terminal phase generator to produce after terminal phaseinitiation a function k(t) =kT+30kT(l l TP/ where k; is the value ofk(t) at terminal phase initiation, kT is the first derivative of M, andTTP is the time from terminal phase initiation to the present, means tofeed back the output voltage e of said second order programming computermeans to its input, and means delaying maximum gain sensitivity of saidcomputer means until the missile is within a predetermined range of thetarget, whereby noisy input radar data is smoothed until maximummaneuverability of the missile is required.

10 Claims, 7 Drawing Figures Unitefl States Patent [191 Schroader et al.

[ 1 June 26, 1973 (on P I QLIMB- CRUISE PHASE GENERATOR TERMINAL PHASEGENERATOR Second Order Smoother Input Converter Seryo Sachem mums ms menor 5 MN kbfibwu kmkbosou k ll l 0M 93am kotwzsu .GEEEQQ 388 A A mM StowINVENTORS \u a ou u S w m a s uskus N i=5 th t IRV/N H. SCH/F0405?MELVIN E. H0564 VINCE, J. GAGE/4N0 W LEO 6. MILLER BY M4 ATTORNEYS LONGRANGE MISSILE PROGRAMMER The present invention relates generally toimprovements in missile guidance systems and the like and moreparticularly to a new and improved guidance system for beam-ridingmissiles wherein a single system capable of multiple flight courseprogramming is rendered adaptable to long range trajectories effectingminimization of missile fuel consumption, maximization of missile rangeand increased probability of successful target kill.

in the field of missile guidance system development, it has been thegeneral practice to employ ground computing devices in conjuntction withcooperating guidance transmitters to guide various beam-riding missilesto their targets. Although such devices have generally served theirpurpose, they have not proved entirely satisfactory under all conditionsof service and operation. In this regard, primary difficultiesencountered have dealt with the minimization of deleterious effects ofget. Hence, those concerned with the development of missiles guidancesystems have long recognized the need for a guidance system capable ofsuch wide adaptability as to enable rapid and precise change-over fromone type of program trajectory to some other more desirable programtrajectory, whichmight be made dependent upon any desired set of inputparameters such as range, angle, or any combination thereof, and whichwould simultaneously avoid. all of the foregoing difficulties commonlyencountered by such systems;

Many of the foregoing difficulties were circumvented by means of theMultiple Flight Course Second Order Programmer disclosed inrelated-copending application Ser. No. 38,408, filed June 23', 1960, US.Pat. No. 3,169,727 by Irvin H. Schroader, Melvin E. Hosea,.and Leo C.Miller and the improvement therein set forth in copending applicationSer. No. 86,267'filed Jan. 3], 1961 1.1.8. Pat. No. 3,164,339, forMissile Programmer Coast Mode Provision by lrvin H. Schoader, Melvin E.Hosea, Leo C. Miller and Frederick F. Hiltz. However effective thesedevices were in improving the accuracy, versatility, and economy ofprevious missile guidance systems, a critical problem yet remainedunresolved by workers in the art. This was the requirement for a longrange missile program having initial flight trajectory phases,independent of target position, so designed as to minimize fuelconsumption and thereby enhance trajectory missile range, and capable ofproviding smooth transition among the various trajectory flight phases.Such a long range program would insure maximum versatility foranyspecific missile type against a large variety of target configurationsand locations, and would minimize the extent to which a wide variety ofstock missiles having different performance characteristics would berequired.

The general purpose of this invention, therefore, is to provide amissile programmer which embraces substantially all the advantages ofpreviously employed missile guidance systems and yet possesses none ofthe aforedescribed disadvantages- To attain the latter, the instantinvention contemplates, among other things, provision of a versatilemissile programming system including a terminal second order programmersmoothing stage and coast provision of the types set forth in copendingapplications Ser. Nos. 38,408 and 86,267, previously mentioned, incombination with a novel arid inventive driving function generator for along range program, the combined system being capable of guidingbeam-riding missiles along prescribed trajectories most suited toconsiderations of missile performance characteristics and target threat,and performing in a manner which insures maximum efficiency and missilerange through the smoothing of input radar data and choice of flightcruising parameters.

The missile guidance system of the instant invention furthercontemplates provision of a second order programmer computing andsmoothing section which acts upon input data so as to cause theelevation and azimuth of the guidance transmitter to approach theelevation and azimuth of the target, prior to target intercept, inaccordance with a prescribed second order equation, the input datadriving function to the elevation portion of the computing section beingof a nature, in accordance with the instant invention, to enable amaximum efficiency long range flight program to be followed. The drivingfunction generator of the instant invention is intended solely forprogramming in the elevation plane alone, since other simpler flightprograms are suitable for programming in the azimuth plane whichrequires only that a smooth transition be ef-. fected. In this regard,therefore, the instant invention modifies the Multiple Flight CourseSecond Order Programmer device set forth in copending applications Ser.Nos. 38,408 and 86,267 by providing a new and improved driving functiongenerator for the elevation portion of the computing section set forthin the latter copending applications, this new and improved drivingfunction generator serving to greatly enhance the range capabilities,and hence the versatility, of the entire second order programmingsystem.

Accordingly, one object of the present invention is the provision of anew and improved missile guidance system.

Another object of the instant invention is the provision of a novelmissile guidance system capable of programming a missile efficientlyover a long range program.

A further object is to provide a new and improved missile guidancesystem capable of quick changeover from a long range guidance program toone of shorter range.

Still another object is to provide a new and improved missile programmerwhich minimizes missile fuel consumption, increases missile range: andinsures maximum probability of target kill.

Yet another object of the instant invention is the provision of a newand improved missile programming device capable of causing missileposition data to approach target position data in a preferred manner toeffect maximum efficiency and probability of target kill with minimumdrag upon the missile during flight.

A still further object of the present invention is to provide a new andimproved missile guidance system incorporating a driving functiongenerator capable of effecting long range trajectory programming.

Another object of the present invention is the provision of an improvedfunction generator for a second order smoothing programmer which will becapable of programming a missile over a long range trajectory.

Other objects and many of the attendant advantages of this inventionwill be readily appreciated as the same becomes better understood byreference to the following detailed description when considered inconnection with the accompanying drawings, wherein:

FIG. 1 is a schematic representation by block diagram of a typicalmissile guidance and control system capable of embodying the device ofthe instant invention;

FIG. 2 illustrates the second order smoother section to which outputinformation from the function generator of the instant invention isdirected;

FIG. 3 illustrates one embodiment of a driving function generator for along range missile program in accordance with the instant invention;

FIG. 4 is illustrative of typical short range flight trajectories;

FIG. 5 illustrates a long range missile flight trajectory obtainable inaccordance with the instant invention;

FIG. 6 illustrates in tabular form integrator status within theprogrammer at various significant times during the long range flightprogram; and

FIG. 7 is a graph illustrating a manner in which guidance sensitivitywithin the second order smoother circuitry may be varied during typicalflight programs.

Multiple flight course second order programmers capable of utilizing thelong range driving function generator of the instant invention comprisebasically an electronic second order smoothing analog computer incombination with a series of servo systems and input and output radarsystems, including all necessary power, cabling and switching necessaryto implement the latter. Such systems are capable of accepting radardata in synchro form and, through the use of suitable follow-up servosystems, of converting such radar synchro data to D.C. signal form forutilization by an electronic analog programming computer section toprovide required missile flight trajectories in accordance withprescribed programming equations to be hereinafter more fully described.Such systems are also capable of converting the computed flight program,in both azimuth and elevation, from conventional D.C. signal outputinformation form, emanating from the computer, into synchro form whichmay then be conveyed to the guidance transmitter radars to command thelatter into proper position. In actual practice, the flexibility of suchguidance system units is even further enhanced through the wide use,wherever possible, of multiple patch panels, the latter being classifiedin accordance with functions handled, such as synchro data, D.C.function, etc.

Typical of desired firing and flight trajectory conditions for a modernguided missile are that the missile be fired at a relatively highlauncher elevation angle, that the missile ascend as rapidly as possibleto a high altitude, and that the missile cruise as long as possible atthis high altitude for maximum engine efficiency, without compromisingthe ability of the missile to intercept the target. As the missileapproaches the vicinity of its designated target, the missile must beprogrammed into a terminal phase, involving a maneuver within theacceleration capabilities of the missile, to produce either a directtarget hit or a near miss accomplishing target kill.

The instant invention contemplates the manipulation of various inputparameters within a novel function generator device in accordance withgeneralized programming equations, to produce an output driving functionsignal for direction as input to a second order smoothing computer. Theinput data is manipulated within the driving function generator in sucha manner as to produce output voltages capable of programming abeam-riding missile through a series of flight phases designated as theclimb phase, the cruise phase, and the terminal phase. The drivingfunction generator of the instant invention handles input data, by meansof a prescribed series of operations, to select for any specific missiletype climb and cruise phases most suited to maximum efficiency andmissile range for that missile. The function generator also initiates aterminal program phase at the proper time and of the proper trajectorytype to insure maximum probability of target kill for the specificmissile riding the guidance beam. Moreover, the novel driving functiongenerator of the instant invention also accomplishes proper programtransition from the climb phase to the cruise phase and from the cruisephase to the terminal guidance phase so as to minimize effects of suchtransition maneuvers upon the missile being guided and thereby at alltimes maintain guidance values of position parameters within theacceleration capabilities of the missile. Long range trajectoriesprogrammed by means of a second order missile flight programmerincorporating the new and improved driving function generator of theinstant invention include climb and cruise phases which are fixed intheir characteristics and independent of any target parameters, with theexception that the duration of the cruise phase, which culminates ininitiation of a terminal guidance phase, is limited in duration by thepredicted time to go before target intercept by the missile.

In the aforementioned copending application Ser. No. 38,408, forMultiple Flight Course Second Order Missile Programmer, two types ofillustrative program trajectories within the scope of the second orderprogramming computer were described. These sample flight programs weredesignated type A and type B. The type A program was specificallydesigned for use with missiles which are total beam-riders, that is,missiles which ride guidance beams all the way to their respectivetargets, whereas the type B program is primarily adapted for use inconjunction with a partially beamriding missile which rides a guidancebeam only to within close proximity of the target and thereafter homesin on the target by means of guidance devices which may be wholly withinthe missile itself and independent of any ground control. The novelfunction generator of the instant invention enables a new and longerrange missile program to be obtained with the second order programmingcomputer set forth in the aforementioned copending application Ser. No.38,408. The latter long range program is, for purposes of illustration,arbitrarily designated as a type C program and is designed for usesolely in elevation plane programming, any other standard program, suchas the type A or type B, being suitable for azimuth plane programming solong as a smooth transition is accomplished.

Referring now to the drawings, which illustrate one embodiment of theinvention, there is shown in FIG. 1 a schematic representation by blockdiagram of a complete missile guidance and control system capable ofprogramming a variety of missile flight trajectories, including that ofthe type C program, best suited to target configuration and missileperformance characteristics.

FIG. 1 shows a search radar 20, incorporating a separate height finder21, which sends out a radar search beam 13 to a target 12 and in turnreceives a reflected signal 14 from the target. Many types of searchradar instrumentation are suitable for utilization in carrying out thelatter function, including search radars having built in height findersor those which incorporate such units separately. The output of thesearch radar and height finder 21 consists of information relating torough values of target azimuth and range and an even rougher value oftarget elevation. The latter output data is then conveyed as inputinformation to a tracking radar 22, which may take a great variety offorms but, for purposes of illustration, is shown here as incorporatinga three coordinate system utilizing train, traverse, and elevation axes.

The target azimuth, target range and target elevation information fromthe search radar 20 and height finder 21 enables the operator of thetracking'radar 22 to either actually look on the target 12 or to throwthe tracking radar into search operation, which is essentially a scanraster of plus or minus a discrete number of degrees about a positionwhich is believed by the operator of the tracking radar 22 to be theapproximate target position as indicated by the rough informationreceived from the search radar system. Other modes of radar systemsfeeding the tracking radar 22 might include such systems as the airforce SAGE concentrated network of defense radars.

The tracking radar 22 transmits its own radar beam 15 to the target 12and receives a reflection 16 therefrom. The output data from thetracking radar 22 is shown as consisting of target elevation, targettrain, target traverse, and slant range from tracking radar 22 to thetarget 12. The latter output information from tracking radar 22 isderived for further use through synchro devices physically located atthe tracking radar unit itself. Shaft rotations about the various axesof the tracking radar 22 are converted by means of such synchro devicesto synchro signals, three wire lines being conventionally embodied foreach synchro, to provide outputs therefrom which are directlyproportional to the number of degrees of radar shaft rotation from anestablished zero reference position.

The synchro output data from the tracking radar 22 is in turn fed to acomputer section 23. The latter tracking radar data is first directed tothe input converter servo section 24 of the computer 23 wherein thesynchro input information is converted by means of servomechanismdevices to electrical signals in the form of D.C. voltages proportionalto the original radar shaft rotations from which the input synchrosignals were derived. Such D.C. voltage signal form is required for useby the programmer section 25 of the computer 23. The programmer section25 utilizes the latter D.C. voltage outputs from the input converterservos as electrical voltage inputs to a computing sectionwhichmanipulates such input voltages on the basis of prescribedgeneralized trajectory equations and produces D.C. output voltages whichare then fed to an output converter servo section 26.

The output converter servo section 26 of computer 23 reconverts the D.C.output voltage signals from the programmer section 25 to synchro signaloutput form for transmission to and utilization by the guidance radartransmitters denoted generally as 27 in FIG. 1 of the drawings. Thelatter guidance radar transmitters 27 are physically located near thetracking and search radars 22 and 20, respectively, or at least within afew hundred feet of the tracking and search radars to prevent theintroduction of severe parallax errors.

The guidance radar 27 transmits a radar signal 17 to the missile 19, butonly in a single direction, that is, guidance radar 27 receivesabsolutely no reflected signal from the missile. The major distinctionbetween the guidance radar transmitters 27 and the tracking radars arethat the guidance transmitters are commanded into position by the outputelevation and azimuth signals from the ground computer section 23. Inthe illustrated embodiment, however, the guidance radar transmitter 27does track in range for the type A and type C programs. In contrast tothe operation of tracking radar 22, the tracking accomplished by theguidance transmitter is not carried out by receiving a signal from themissile constituting a reflection of an original signal generated in theguidance transmitter itself. On the contrary, missiles utilizing thetype A and type C program trajectories carry a beacon 28 incorporatedinto the missile and which is triggered by the guidance beam 17 from theguidance transmitter 27 to generate a beacon signal 18 of its own. Thelatter beacon signal 18 is directed from the missile 19 to the guidancetransmitter 27, thetime of delay of arrival of the beacon signal at theguidance transmitter being a measure of the slant range to the missile.

For the type B program set forth in the aforementioned copendingapplication Ser. No. 38,408, which program is designed for utilizationsolely by missiles which incorporate separate homing systems, theprogram flight trajectory is not dependent upon input information to thecomputer section 23 relating-to the difference between target slantrange and missile slant range, and hence, the guidance transmitter 27 isnot required to track in range for such a program.

For the type A and type C programs, therefore, the missile slant rangeinformation received by the guidance transmitter 27 is fed back into thetracking radar 22 to enable the latter unit to direct an output to thecomputer section 23 which is the difference between slant range to thetarget and slant range to the missile, whereas for the type B program,with homing, there is no tracking in range by the guidance transmitter27 nor any feedback of such information from the guidance transmitter tothe tracking radar 22, and, therefore, in the latter instance the outputof the tracking radar 22 would be simply slant range to the target.

Missiles utilizing the multiple flight course programmer of the instantinvention must, of necessity, be beam-riders. A missile 19 of this typeis captured by the radar beam 17 emanating from the guidance transmitter27 so that the missile 19 is caused to follow the beam as the beam movesin accordance with the programmed flight trajectory. Servomechanismdevices within the missile itself steer the missile in accordance withthe transmitted guidance signals so that the missile 19 is caused toalways remain within the guidance beam after capture, provided theguidance beam moves in such a manner that the missile capabilities oflinear velocity and lateral acceleration are not exceeded.

In actual operation, prior to launching, the operator of the missileguidance and control system elects, in accordance with the nature of themissile to be tired, a suitable program trajectory i.e., for a longrange target the type C program of the instant invention would bechosen. The operator then proceeds to orient various switches in theguidance transmitter in accordance with the program choice made, e.g.,for tracking in missile range or not by the guidance transmitter, andsimultaneously operates switches in the programmer section 25 ofcomputer 23 to select proper constants and input data channels for thechosen program.

As previously outlined, typical requirements for a modern guided missileare that the missile be fired at a relatively high launcher elevationangle, rapidly ascend to a high altitude, cruise as long as possible atthis altitude for maximum engine efficiency, and then dive towards thetarget in a maneuver within the acceleration capabilities of themissile, to produce a target kill. Two types of trajectories, suitablefor these purposes, have been previously evolved and described. The typeA program was designed for a totally beam riding missile carrying abeacon capable of relaying missile range information to the guidancetransmitter, in the manner utilized for the type C program of theinstant invention, and the type B program was designed for a partiallybeam-riding missile, without beacon, which utilizes separate homingsystems to intercept the target.

After the missile is initially fired at a relatively high launcherelevation angle, a discrete period of time elapses before capture of themissile by the guidance beam is accomplished. Thereafter, E theelevation of the guidance transmitter, must approach E the elevation ofthe target, in accordance with prescribed programming equations.

FlG. 4 of the drawings illustrates the trajectory shapes found desirablein those instances where the type A and type B programs are utilized. Itwill be noted from FIG. 4 that, whereas the type A program causes themissile to intercept the target in a direct collision course, the type Bprogram causes the missile to approach asymtotically to the line ofsight from the tracking radar to the target prior to collision. Both thetype A and type B programs disclosed in the aforementioned copendingapplication Ser. No. 38,408 are of the medium range variety, that is,they are unsuited to long range trajectories. In this regard, theinstant invention provides a novel driving function generator capable ofdirecting a new type of input to the second order programming computerto enable an output trajectory therefrom suitable for long range flightprograms.

For the purpose of analyzing and specifying missile performance duringthe type C program, as controlled and guided by a novel second orderprogramming computer system, it isnecessary to first define the flighttrajectory, as represented by the output data emanating from thecomputer section, in terms of specific mathematical system equations andspecified input parameters to the computer section utilizing the latterequations. The system equations utilized by the second order programmerhave been previously disclosed in copending application Ser. No. 38,408to be and 1-! 7 W Y W 2 to: (e,, e,-)dt constant [=6 where e, is theoutput data from said computer,

a, is the input data to said computer, e], is the first derivative of e,

m is the gain sensitivity factor of the computer,

(7' is a constant,

P is the present time, and

G is the time of guidance initiation,

An important feature of the second order computer circuitry utilized forcomputing the various program trajectories in accordance with the aboveequations is the manner in which the value of w,,, the gain sensitivityfactor, is varied. A low value of w allows e, to change only slowly andto be relatively insensitive to changes in e,-, the input data. On theother hand, a high value of (0,, allows e, to change rapidly and to bemore sensitive to fluxuation in e,. Therefore, the manner in which w,the gain sensitivity factor is programmed is of prime importance insofaras the versatility and smoothing efficiency of the second orderprogramming computer system is concerned.

It has been determined empirically that adequate smoothing of noisyinput data and desired flight trajectory accuracy will be realized ifthe gain sensitivity factor, (0,, is programmed in accordance with theequation 0),, c/(Tpi c) where Tpi is the time from present to interceptand c is a constant. Such an empirical programming equation for winsures values of gain sensitivity lying between zero and unity andeliminates the situation where a gain sensitivity of infinity would berequired, the latter case being one which would obtain if the gainsensitivity constant c were omitted from equation (3). The specificvalues of the constant c in equation (3) for w is generally determinedfor any particular missile by means of simulator analysis, values of cbetween 3.5 and 4.5 being fairly common for typical modern missilespresently in use. The value of c, however, may assume any desired formfor presently existing or subsequently developed future missiles and,therefore, the variability of c-values provides for a wide range ofadaptability. By way of example, FlG. 7 of the drawings illustrates themanner in which (o the gain sensitivity factor, is varied in accordancewith equation (3) for a value of c 4.

The type C program of the instant invention is depicted in FIG. 5 of thedrawings. The latter trajectory is shown to comprise climb and cruisephases and a terminal guidance phase. Essentially, the climb and cruisephases are combined into a single phase which is substantiallyindependent of target position and effects a smooth transition from theclimb phase to the cruise phase. The climb trajectory is fixed and doesnot depend upon the target position at all. The cruise phase stretchesor shrinks in length, that is, the cruise phase has a varying period ofduration to suit target parameters, and is essentially a trajectory atconstant cruising altitude, for maximum efficiency, compensated by aslight droop to account for the earths curvature. The type C programalso enables a smooth transition from the combined climb-cruise phase tothe terminal guidance phase at the point of terminal guidanceinitiation. At this latter point, it was required that not only missilepositions on both sides of the transition point, but rates of change ofposition as well, had to match in order to avoid unreasonable maneuverson the part of the missile and the introduction of instability into themissile flight control system. The resulting type C program shown inFIG. of the drawings greatly extends the range capabilities of missileswhich would normally be capable of using the type A or type B programsonly for targets at medium range. One additional distinction, however,remains in comparing the type C program with the trajectories of thetype A and type B varieties. The type C program is utilized solely inthe elevation plane and uses any other standard transition in theazimuth plane such as the type A or type B azimuth programs. On theother hand, whenever the type A or type B programs are utilized in theelevation plane for medium range targets the same type programs areutilized in the azimuth planes as well.

Referring now to FIG. 2 of the drawings, which illustrate in combinedblock diagram and schematic form a long range programmer of the secondorder type, the instant invention is shown to comprise a new andimproved driving function generator 207 whose output is directed as aninput to an input amplifier 201 of a second order programmer computingand smoothing network, to enable the latter to produce output elevationguidance signals capable of directing a beam-riding missile in a flighttrajectory involving minimum fuel consumption and drag upon the missilefor maximum efficiency and range. Additional parameters are derived froman input converter servo section 24 and are also directed as inputs tothe second order computer input amplifier 20]. The second orderprogramming computer and smoother is shown comprising the series of fouramplifiers indicated as 201, 202, 203, and 204, respectively, andincorporating coast mode provisions, all of which have been fullydisclosed and claimed in the aforementioned copending applications Ser.Nos. 38,408 and 86,267 These features will be only briefly outlinedhere, since the invention is deemed to reside primarily in the new andimproved function generator which enables the second order programmingcomputer and smoother to program a long range type C trajectory.

Amplifier 201 is a conventional D.C. analog type summing amplifier, wellknown in the art and commercially available. Amplifiers 202, 203 and 204are conventional integrating amplifiers with initial-condition circuits.The combined input to integrating amplifier 204 is s the firstderivative of e the output of integrating amplifier 204 being e,, Thelatter quantity is directed to the output converter servo section 26prior to transmission to the guidance transmitter 27 and is alsosimultaneously fed back as an additional input to computer inputamplifier 201 which receives the input data e the nature of which isdetermined by the desired output flight trajectory program. The input toamplifier 201 is thus e, e, and the output, in view of the inherent 180phase shift which takes place in the amplifier 201 and the resultingreversal in sign, is therefore e, e, or e For purposes of solvingequation (2), the quantities me and (0, 6 must be obtained, and theseoperations are accomplished as described below.

The output of amplifier 201, which is e is fed to a potentiometer 205,the shaft position of which is equal in value to (0,, the gainsensitivity factor. Hence, since the input to potentiometer 205 is e theoutput therefrom is equal to 0),, multiplied by e or (o e The latterquantity isfed as an input to the initial-condition circuit ofintegrating amplifier 202 and is also simultaneously directed to asecond potentiometer 206 whose shaft position is like-wise adjusted tothe value of w The input to integrating amplifier 202 is short-circuitedto ground. The output voltage from the potentiometer 206 is w e thelatter voltage being fed directly as input to integrating amplifier 203.A switch 209 is also provided in the input circuit to integratingamplifier 203 to enable switching from the cafe input to a terminalwhich short-circuits the input to ground.

The mechanical output proportional to a) which is utilized to controlthe shaft positions of potentiometers 205 and 206, is obtained from an0),, circuitry section 30 which programs the gain sensitivity factor0),, in accordance with equation (3) and is fully disclosed in relatedcopending application, Ser. No. 38,408, filed 23 June 1960, for MultipleFlight Course Second Order Programmer, by Irvin H. Schroader, Melvin E.Hosea and Leo C. Miller. For purposes of the instant discussion, it willsuffice to say that w the gain sensitivity factor, is limited to valuesbetween zero and unity, in accordance with equation (3), and since theshaft positions of both potentiometers 205 and 206 are at all times setto the value of w therefore the respective outputs from the latterpotentiometers are functions of the input voltages across thepotentiometers and directly proportional to 0),, It is realized ofcourse that the use of the second potentiometer 206 connected in themanner shown to obtain (0,, is merely a close approximation method sincethe effect of the second potentiometer 206 is to load the firstpotentiometer 205. Hence, to increase the accuracy of such anapproximation approach, the second potentiometer 206 is supplied with asomewhat higher value of total resistance then that of the firstpotentiometer 205.

It has been established that the input to the initialcondition circuitof integrating amplifier 202 is w,,e and the input to integratingamplifier 203 is m e Passage of the signal through the initial-conditioncircuit of amplifier 202 merely serves to provide a reversal in signthrough inherent phase shift. Therefore, the output from integratingamplifier 202 is w,,e The gain of integrating amplifier 203 is adjustedto provide multiplication by the factor a in equation (2). Thus, theoutput of integrating amplifier 203 is equal to [=P a- I afiedtconstant.

The output from integrating amplifier 202 is directed to one input ofintegrating ampiifier 204 while the output of integrating amplifier 203is directed to a second input of the summing integrator 204. The gain ofthe inputchannel receiving the w,,e' input is adjusted to a value of twoto provide an equivalent input of 2w,,e Thus, the input circuit tointegrating amplifier 204 consists essentially of the outputs ofamplifiers 202 and 203 modified by input gains in respective channels ofthe integrator 204, the sum of these terms being equal to the firstderivative of e,,, or 2 in accordance with equation (2). Hence, theoutput from integrating amplifier 204 is e,, which is directed asfeedback to one input channel of amplifier 201, and simultaneouslydirected to the output converter servo section 26 for subsequentconveyance to the guidance transmitter 27.

The coast mode provisions provided in integrating amplifiers 202 and 203enable integrating amplifier 202 to be switched from theinitial-condition state to the compute state and simultaneously toswitch the input to integrating amplifier 203, which is already in thecompute state, from the 6 input condition to the short-circuit to groundcondition, both of these operations being accomplished by suitablerelays upon loss of target track by ground radars. The coast modeprovisions are set forth in detail in copending application Ser. No.86,267 filed Jan. 31, 1961, for Missile Programmer Coast Mode Provision,by Irvin H. Schroader, Melvin E. Hosea, Leo C. Miller and Frederick F.Hiltz.

It should be noted that the second order computing and smoothingcircuitry described above allows e,, to gradually approach e,, untilactual intercept with the target, in a manner and degree dependent uponthe rapidity with which e can change, the latter being controlled by themagnitude of the gain sensitivity factor (0,, which, in turn, controlsthe shaft position settings of the potentiometers 205 and 206. If m isallowed to reach its maximum value of unity, then e can approach e, veryrapidly since the feedback loop gain is very high, whereas if the oshaft position settings of potentiometers 205 and 206 are near theirlower limits, that is, with (0,, at a value of considerably less unity,then the feedback loop gain is very low and s will follow input data e,rather slowly and with a substantial lag. One purpose, therefore, of thesecond order programming computer is to cause e, to approach e, from aninitial value of e and proceed through a transient phase whose natureand time duration is controlled by the manner in which the gainsensitivity factor, (o is programmed. A large value of (0,, increasesthe tightness with which e can follow e, and reduces the transient errordue to rapid variation in input voltages. On the other hand, a low valueof w, provides heavy smoothing of noisy radar data. In practice,therefore, the manner of programming w in accordance with equation (3)is a compromise between the suppression of noise on the input data e toprevent vibration of the missile wing flaps and consequent increaseddrag and possible damage to missile wing servos, and maximum probabilityof target kill. Thus, 107 is programmed in time in such a manner as toenable e to follow e, to an increasingly close tolerance as actualcollision with the target approaches, a large value of a) being utilizedto increase the tightness of following during the latter portion ofprogrammed flight when the missile is close to the target, whereas asmall value of w is utilized for the initial portion of the program toprovide heavy smoothing of noisy radar input data.

The preceeding has been a discussion of the basic second orderprogrammer computing and smoothing network. By varying the nature of theinput data e, to the computer input amplifier 201, the nature of theoutput flight trajectories represented by e, can be molded to conformwith any one of a number of programs. The type A and type B programs andmethods for obtaining the latter have been previously disclosed indetail in copending application Ser. No. 38,408. The long range type Cprogram and the function generator necessary for obtaining the latterprogram form the basis of the instant invention and are next discribed.

The shape of the type C long range program trajectory is illustrated inFIG. 5 of the drawings. The type C trajectory is shown to comprise acombined climbcruise phase wherein the missile is initially launched ata high launcher elevation angle, is captured by the beam emanating fromthe guidance transmitter, continues to rise in a climb path which has asmooth transition into a maximum efficiency cruise phase ofapproximately constant altitude with slight droop to account for theearths curvature, and at a prescribed point determined by the rate atwhich the missile is closing on the target, a smooth transition isaccomplished to a terminal phase ultimately leading to target intercept.

Referring again to FIG. 2 of the drawings, the nature of the outputtrajectory signals 2,, from the second order programming computer andsmoother is governed by the nature of the input data function e, to thecomputer input amplifier 201. As previously set forth in copendingapplication Ser. No. 38,408, the nature of the input data function forthe type A and type B medium range flight trajectories are for the typeB program and i T r u) for the type A program where E Elevation of theTarget 0 Slant Range to the Target 0,, Slant Range to the Missile KProgramming constant Basically, the long range type C program is similarto the type A medium range program and requires an input drivingfunction to input amplifier 201 of the second order smoothing computerwhich may be broadly described as follows:

r ET 1-' Ml e, E F (d) where K(t)= time varying programming factor andF(d) output of driving function generator [DT DM] A comparison ofequation (6) for the type C program with equation (5) for the type Aprogram, reveals that in order to realize the long range type C program,the co-efficient of the D, D term must be a suitable function of timek(t) rather than a constant K as utilized in the type A program. Byvarying the nature of the programming factor k(t) the nature of theinput data function e, to the second order computer can be tailored toprogram the missile through the climbcruise phase and the terminalphase.

A major requirement of the long range type C program is the smoothtransition between the various flight phases of the program. The latteris necessary to avoid the introduction of heavy transients andconsequent instability in the guidance system and also to preventunnecessarily hard maneuvers on the part of the missile with inherentresulting loss in efficiency and range capabilities. In this regard,therefore, the following stringent requirements in addition to that ofsmooth transition between the climb and cruise phases are required:

where k value of k(t) at end of climb-cruise phase,

k value of k(t) at initiation of terminal phase,

The manner in which k (t) is varied in order to accomplish the desiredflight stages for the long range type C program is described below.

The climb and cruise phases are combined into a single transient withinherent smooth transition in accordance with the requirements ofequations (8) and (9). The manner in which k(t) is varied for theclimb-cruise phase has been empirically determined F(t) (bd a DM)/( DM)and F(z) Program Variable defining the combined climb-cruise phase,

P present time,

G time of guidance initiation,

a, b, d Constants to be specified.

The resulting climb-cruise phase, as illustrated in FIG. of the drawingsincludes a climb trajectory, which is independent of target parameters,and a cruise phase which is essentially at constant altitude with slightdroop to compensate for the earth s curvature and which varies in periodof duration in accordance with the rate at which the missile and targetare closing in range. In other words, the duration of the cruise phase,which terminates in terminal phase initiation, is dependent upon D Dhaving diminished to a specified value.

To obtain the terminal phase flight portion of the type C long rangeprogram trajectory, the value of k(t) at terminal phase initiation isfrozen at the value it had at the end of the climb-cruise phase and isthereafter allowed to decay exponentially over a specified timeinterval. The resulting terminal phase, therefore, is a modified form ofthe type A program, differing only in that the coefficient of the D 0,,term is a slowly varying function of time rather than the constant k inequation (5).

It will be noted, referring to FIG. 5 of the drawings, that the terminalphase is not limited to a dive upon the target from above, but can alsorise from the cruise level and intercept high altitude targets frombelow. The manner in which k (t) is varied during the terminal phase tosatisfy the above stated condition has been determined empirically to bek (r) =k 3o [to 1 e[ T /30 1 where T Time from terminal phase initiationto I present.

It will be noted from equation (12) that, at the beginning of theterminal phase, the second term in equation (12) reduces to zero and,therefore, equation (8) is satisfied. Taking the first derivatives ofboth sides of equation (12) will also reveal that the requirement setforth in equation (9) is also satisfied.

The circuitry for the novel F(d) function generator 207, in FIG. 2 ofthe drawings, is depicted in detail in FIG. 3 of the drawings and isshown to comprise several sets of integrators which are in the computeor initial-condition states at various times during the type C programin order to satisfy the requirements of equations (6) through (12). Inthis regard, FIG. 6 of the drawings, which is a table of integratorstatus, serves to clarify the condition of each integrating amplifier inboth thb driving function generator and the second order smoother at alltimes during programmed flight.

The multiple flight course second order programming smoother set forthin copending applications Ser. Nos. 38,408 and 86,267 is merely utilizedas a smoother in this instance and is designated broadly as a unit 29 inFIG. 3 of the drawings, the major portion of the programming beingaccomplished by manipulations in the novel function generator of theinstant invention which varies the nature of k(t) in equation (6).

Referring now specifically to FIG. 3 of the drawings, the drivingfunction generator of the instant invention directs a function F(d) tothe input circuit of the second order smoother 29 and acts inconjunction with an E signal derived from the input converter servosection 24 to produce a total input data function e,- as set out inequations (6) and (7). The equation (11) form of F(!) is rearrangedbelow.

It will be noted in FIG; 3 that amplifier gains of unity have beenarbitrarily assigned to all of the channels in the various amplifiersand integrators utilized in the driving function generator of theinstant invention. However, it is to be understood that the gains inthese channels may be varied by established computer programmingprocedures for scale factoring purposes.

It will be observed from FIG. 3 of the drawings that the overall drivingfunction generator of the instant invention comprises basically a pairof function generators in series. This combination consists of aclimbcruise phase generator in series with a terminal phase generator.In actual operation, as will be subsequently shown, the terminal phasegenerator acts essentially as a pass through device during theclimb-cruise phase and does not modify F(t) the output of theclimbcruise phase generator, in any manner.

The climb-cruise phase generator system for developing values of thefunction F(t) is described as follows:

It is assumed that the function F(t) in the form set forth by equation(13) has already been generated and a feedback loop circuit is thenprovided for actually generating the quantity F(r). The output signalfrom the climb-cruise phase generator is F(t) and this signal isdirected to a b potentiometer 108 which is shown grounded at one end.The slider arm of potentiometer 108 is adjusted to providemultiplication by the factor l/b and this output is in turn directed toone input channel ofa summing integrator 102 having three inputchannels.

In addition, a second potentiometer 109 is provided with a potential ofl volts impressed upon one terminal, the other side of the potentiometerbeing grounded. The slider arm position of potentiometer 109 is adjustedto provide the value of the constant factor a/b, this output being thendirected to the second input channel of the integrating amplifier 102.The output from integrating amplifier 102 is directed back to a thirdinput channel of amplifier 102 so that the output is caused to followits input with inherent 180 phase shift and reversal in sign. The outputof amplifier 102 is therefore F(t) a/b The integrating amplifier 102 isutilized in place of a normal summing amplifier in order to eliminateoscillation by increasing the damping rate of the system. Reference toequation (l3) reveals that a product involving the quantity D alone as afactor is required. However, the factor D is not available in theMultiple Flight Course Second Order Programmer, disclosed in relatedcopending application Ser. No. 38,408, as a separate entity fortransmission to the computer. However, both the quantities D, and D Dare available and these quantities may be utilized, as shown below, toobtain multiplication by the factor D alone.

Therefore, the output from integrating amplifier 102 is directedsimultaneously across two potentiometers 110 and 111, respectively, theslider arms of potentiometers I and 111 being controlled in accordancewith the aforementioned quantities D and D D respectively, to providemultiplication by these factors.

The constant d in equation (13) is obtained by means of integratingamplifier 101 in FIG. 3. Integrator 101 is provided to insure that F(t)is equal to E the initial condition elevation angle of the guidancetransmitter, at guidance initiation. Therefore, summing integrator 101receives two inputs, one of these being F(t) and the other being E Theoutput of integrating amplifier 101 is d in equation (13). This latteroutput d is directed as one input to summing amplifier 103. A secondinput to this same amplifier 103 is received from the output ofpotentiometer 110 which has previously been shown to be [F(t) a]D /b.The output from summing amplifier 103 is, therefore, the sum of itsinputs or which is directed as an input to one channel of summingamplifier 104. The second input channel of summing amplifier 104receives the output from potentiometer 111, which has previously beenshown to be and, therefore, the output from amplifier 104 is equal tothe sum of its inputs or F(t) in accordance with equation (13).

Between launching of the missile and actual guidance initiation, summingamplifier 101 is in the compute state and, therefore, the feedbacknetwork composed of integrating amplifier 101 and the two followingamplifiers 103 and 104 forces F(t) to take on the value of E at theinstant guidance begins, due to the feedback of the output fromintegrator 101 to its input by way of amplifiers 103 and 104. Therefore,the subsidiary loop comprising amplifiers 101, 103 and 104 forces F(t)to equal E at guidance initiation. Following guidance initiation,integrating amplifier 101 is thrown into the Hold mode which essentiallyserves to disconnect its inputs and cause the integrating amplifier 101to maintain its last output value, which is equal to the desired valueofd in equation (13 The status of integrator 101 at all times during theflight program is evident from FIG. 6 of the drawings.

The output voltage -F(t) from amplifier 104 of the climb-cruise phasegenerator is fed to one input channel of the input summing amplifier 105of the terminal phase generator shown in FIG. 3 of the drawings. Inputamplifier 105 simultaneously receives a signal E the elevation of thetarget, from the input converter servo section 24. The output from inputamplifier 105 is directed into the initial-condition circuitry ofintegrator 106, the latter integrator serving only to effect phaseinversion of the output signal from amplifier 105. The output fromamplifier 106 is, in turn, directed as input to integrating amplifier107 whose output is k(t) which is fed across potentiometer 113. Theslider arm position of potentiometer 113 is controlled in accordancewith the D D signal. The output across potentiometer 113 is F(d) whichis fed back to an input channel of summing input amplifier 105 of theterminal phase generator. This latter feedback causes the output F(d) tofollow the input. Neither the D D multiplication nor the integration byintegrator 107 actually effect the value of F(d) due to the feedbackloop, since we are dealing with an extremely slowly varying functionduring the climb-cruise phase. Therefore, k (t) takes on the values setforth in equation (10) and the output F(d) is equal to the input toamplifier 105 with a reversal in sign and, therefore, F(d) equals F(t) Ewithin the limits imposed by the velocity lag of the first orderfeedback circuit involved. Therefore, substituting this value of F(d) inequation (7) we find that e, F(t) except for the small time constantinvolved, which is of minimum significance here since we are dealingwith a relatively slowly varying D D function. In this regard,therefore, during the climb-cruise phase the terminal phase generatordoes not modify the input it receives from the climb-cruise phasegenerator and essentially acts merely as a pass-through device.

Referring now to the terminal phase generator shown in FIG. 3, it hasbeen determined empirically that a terminal phase of approximatelyseconds is sufficiently long to allow a missile to dive or rise to atarget on the deck without exceeding missile performancecharacteristics. The terminal phase, therefore, begins approximately 100seconds before anticipated intercept of the target by the missile. Thismay be expressed mathematically as follows:

D D 100 (D, D

At this time, a signal, for instance that from amplifier 105, tripsrelays, a switching circuit, a gate circuit, or any other meanswell-known in the art, in accordance with the table of integrator statusset forth in FIG. 6 of the drawings, to initiate the terminal guidancephase.

At terminal phase initiation, integrator 106 is changed from the initialcondition state to the compute mode of operation, which effectivelyserves to disconnect the F(t) function from passing through theintegrator 106 and, therefore, renders the output signal from theclimb-cruise phase generator and amplifier 105 ineffective upon theprogram trajectory beyond this point.

The output from integrator 106 immediately after terminal phaseinitiation is k(t) which has the same value that it had immediatelypreceeding terminal phase initiation, thus fulfilling the previousrequirement set forth in equation (9). Similarly, the output ofintegrator 107 is k(t) and is the same value for just prior to as justafter terminal phase initiation, thus satisfying the second transitionrequirement set forth in equation (8).

However, the output of integrator 106 is also directed across apotentiometer 112 whose slider arm position is set to a value of 1/30 or0.33, this output being in turn directed to the input circuit ofintegrating amplifier 106. The result of this feedback aroundintegrating amplifier 106, at reduced gain via potentiometer 112, issuch that a time constant of 30 seconds is established and k(t) willdecay to zero with the latter time constant. Thus, the output ofamplifier 106 and hence the input to integrating amplifier 107, which isk(t), will be a slowly decreasing function, and the output fromamplifier 107 will be k(t) in accordance with the requirements ofequation (12). The latter is verified mathematically as follows:

which merely serves to state in mathematical form what is obvious fromFIG. 3 of the drawings, namely that the output from integrator 107 isequal to its initial value plus the integrated sum of its input. In thelatter instance, integrator 106 sets the limitations on the input tointegrator 107 as follows:

Substituting the value of k(t) from equation (18) into equation (17)yields which is in agreement with equation (12). Thus, the output fromintegrating amplifier 107 is k(t) and is directed accordingly across theD D potentiometer 113 to produce a signal F(d) in accordance withequation (7). As pointed out previously, the major distinction betweenk(t) and K in equation for the type A program is that k(t) is a slowlyvarying function of time rather than being a constant. The output fromthe terminal phase generator, F(d), is directed as one input to thesecond order smoother 29. A switch is also provided in the linedirecting F(d) to smoother 29 so that the input F(d) may be disconnectedat will and the smoother may be put through a standard type B program.

Although w for the type C program is theoretically programmed inaccordance with equation (3), it has been determined in actual practicethat the introduction of the term k(t) [D -D during the terminal phase,as part of the input data e, to the second order smoother 29, causes e,to vary very rapidly and, therefore, in order to prevent e, from lagginge, by too great a margin, a higher value of the gain sensitivity factor00,, is desired for the initial portion of the type C program flighttrajectory than would ordinarily be obtained by programming (0,, inaccordance with equation (3). Therefore, (o is held constant at a highervalue, of the order of magnitude of 0.1, until the latter value isreached by normal programming in accordance with equation (3), thelatter condition occurring approximately 30 to 40 seconds before targetintercept. Thereafter, a), is programmed in accordance with equation (3)just as for the standard type B program. The latter variation in themanner in which (1),, is programmed is depicted graphically in FIG. 7 ofthe drawings.

The reason, as previously stated, for manipulating w, in the abovemanner is to strike a suitable compromise between keeping down noise andminimizing missile wing servo damage balanced against desirable closetracking of the target. To accomplish the latter, therefore, w isinitially held low at a value of 0.1 until the missile is withinapproximately seconds of intercepting the target, at which point (0,, isallowed to rapidly approach unity as the missile nears the target, sincethe increased guidance sensitivity enabled thereby allows the missile tomaneuver much more readily in following the target closely. In otherwords, the limits imposed by the velocity lag of the second orderfeedback circuit involved becomes considerably less critical as thevalue of m, is increased, a condition which is extremely valuable duringthe latter portion of the flight program when the missile is maneuveringin close quarters with its designated target.

The novel driving function generator of the instant invention, when usedto provide an input to a second order smoother of the type set forth incopending applications Ser. Nos. 38,408 and 86,267, enhances theversatility of the latter programmer even further by enabling extendedrange capabilities for modern missiles presently in use. The economicaland tactical advantages of such a system should be obvious.

Obviously, many modifications and variations of the present inventionare possible in the light of the above teachings. It is therefore to beunderstood, that within the scope of the appended claims, the inventionmay be practiced otherwise than as specifically described.

What is claimed is:

1. In an apparatus for controlling the flight trajectory of a guidedmissile, second order programming computer and smoother means formanipulating input parameters in accordance with the relations and wheree,, is the output data from said computer,

e. is the input data to said computer,

is the first derivative of e,,-

m is the gain sensitivity factor of the computer,

E is the elevation of the target,

' is a constant,

P is the present time,

G is the time of guidance initiation,

k(t) is a time varying programming factor and F(d) is the output of aninput driving function generator, a first input source of voltage forsaid second order programming computer means relating to E drivingfunction generator means F(d) electrically coupled to and directed as asecond input to said second order programming computer means, saiddriving function generator means comprising a climb-cruise phasegenerator in series with a terminal phase generator, means within saidclimb-cruise phase generator to produce an output function where F(t) isthe program variable defining the climb and cruise phases,

D is the slant range to the missile,

E is the initial condition elevation angle of the guidance transmitter,and

a and b are constants, the output of said climb-cruise phase generatorbeing directed as a first input to said terminal phase generator, meanselectrically connected to the input of said terminal phase generatorproviding a second input to said terminal phase generator relating to Efeedback means electrically connected to the output of said terminalphase generator to feed back the output F(d) of said driving functiongenerator as a third input to said terminal phase generator, meanswithin said terminal phase generator for acting upon said first, secondand third inputs prior to terminal phase initiation to produce an outputfunction means within said terminal phase generator to renderineffective said first, second and third inputs upon terminal phaseinitiation, means within said terminal phase generator to produce afterterminal phase initiation a function k(t) k 30 k (l eTTP where k, is thevalue of k(t) at terminal phase initiation,

k is the first derivative of k and T is the time from terminal phaseinitiation to the present, means to feed back the output voltage e ofsaid second order programming computer means to its input, and meansdelaying maximum gain sensitivity of said computer means until themissile is within a predetermined range of the target, whereby noisyinput radar data is smoothed until maximum maneuver ability of themissile is required.

2. The apparatus of claim 1 including means to vary the gain sensitivityfactor a) of the second order computer means in accordance with therelation 0),, c/( Tpl of) where T,., is the time remaining untilintercept of the target by the missile, and

c is a constant 3. The apparatus of claim 1 including means todisconnect the output F(dsaid driving function generator means from theinput of said second order computer means to enable a medium rangeflight trajectory to be programmed.

4. The apparatus of claim 1 including means to delay terminal phaseinitiation until where D is the slant range to the target D is the slantrange to the missile,

D} is the first derivative of D and D is the first derivative of D 5.The apparatus of claim 1 including means to limit the minimum value ofthe computer means gain sensitivity factor a) to a value of 0.1.

6. The apparatus ofa claim 2 including means to limit the minimum valueof the computer means gain sensitivity factor to a value of m 0.1.

7. The apparatus of claim 2 wherein the value of c is in the range from3.5 to 4.5.

8. The apparatus of claim 6 wherein the value ofc is in the range from3.5 to 4.5.

9. The apparatus of claim 6 including means to delay terminal phaseinitiation until D D 100 (D D where D is the slant range to the target,

D is the slant range to the missile,

D} is the first derivative of D and D}, is the first derivative of D 10.In a missile programming system utilizing a second order computingdevice, driving function generator means electrically connected to theinput of said second order computing device whose electrical output isdirected as an input to said second order computing device, said drivingfunction generator means comprising a climb-cruise phase generator inseries with a terminal phase generator, means within said terminal phasegenerator to cause said terminal phase generator to act merely as a passthrough device for the signal generated by said climb-cruise generatorduring the climb-cruise phase, means within said terminal phasegenerator to render ineffective upon terminal phase initiation the inputfrom said climb-cruise phase generator to said terminal phase generator,and means for effecting a smooth transition from said climb-cruise phaseto said terminal phase.

1. In an apparatus for controlling the flight trajectory of a guidedmissile, second order programming computer and smoother means formanipulating input parameters in accordance with the relations
 2. Theapparatus of claim 1 including means to vary the gain sensitivity factoromega n of the second order computer means in accordance with therelation omega n c/(Tp1 + ) of ) where TPI is the time remaining untilintercept of the target by the missile, and c is a constant
 3. Theapparatus of claim 1 including means to disconnect the output F(dsaiddriving function generator means from the input of said second ordercomputer means to enable a medium range flight trajectory to beprogrammed.
 4. The apparatus of claim 1 including means to delayterminal phase initiation until DT - DM 100 (DT-DM) where DT is theslant range to the target DM is the slant range to the missile, DT isthe first derivative of DT and DM is the first derivative of DM .
 5. Theapparatus of claim 1 including means to limit the minimum value of thecomputer means gain sensitivity factor omega n to a value of 0.1.
 6. Theapparatus of a claim 2 including means to limit the minimum value of thecomputer means gain sensitivity factor to a value of omega n 0.1.
 7. Theapparatus of claim 2 wherein the value of c is in the range from 3.5 to4.5.
 8. The apparatus of claim 6 wherein the value of c is in the rangefrom 3.5 to 4.5.
 9. The apparatus of claim 6 including means to delayterminal phase initiation until DT - DM 100 (DT - DM) where DT is theslant range to the target, DM is the slant range to the missile, DT isthe first derivative of DT, and DM is the first derivative of DM
 10. Ina missile programming system utilizing a second order computing device,driving function generator means electrically connected to the input ofsaid second order computing device whose electrical output is directedas an input to said second order computing device, said driving functiongenerator means coMprising a climb-cruise phase generator in series witha terminal phase generator, means within said terminal phase generatorto cause said terminal phase generator to act merely as a pass throughdevice for the signal generated by said climb-cruise generator duringthe climb-cruise phase, means within said terminal phase generator torender ineffective upon terminal phase initiation the input from saidclimb-cruise phase generator to said terminal phase generator, and meansfor effecting a smooth transition from said climb-cruise phase to saidterminal phase.